Bodendorfer N, Thiemann T, Thurn A (2014)

**Publication Status:** Published

**Publication Type:** Journal article

**Publication year:** 2014

**Publisher:** IOP PUBLISHING LTD

**Book Volume:** 31

**Journal Issue:** 5

**DOI:** 10.1088/0264-9381/31/5/055002

In this paper, we generalize the treatment of isolated horizons in loop quantum gravity, resulting in a Chern-Simons theory on the boundary in the four-dimensional case, to non-distorted isolated horizons in 2(n + 1)-dimensional spacetimes. The key idea is to generalize the four-dimensional isolated horizon boundary condition by using the Euler topological density E-(2n) of a spatial slice of the black hole horizon as a measure of distortion. The resulting symplectic structure on the horizon coincides with the one of higher-dimensional SO(2(n + 1))-Chern-Simons theory in terms of a Peldan-type hybrid connection Gamma(0) and resembles closely the usual treatment in (3 + 1) dimensions. We comment briefly on a possible quantization of the horizon theory. Here, some subtleties arise since higher-dimensional non-Abelian Chern-Simons theory has local degrees of freedom. However, when replacing the natural generalization to higher dimensions of the usual boundary condition by an equally natural stronger one, it is conceivable that the problems originating from the local degrees of freedom are avoided, thus possibly resulting in a finite entropy.

Norbert Bodendorfer
Chair for Theoretical Physics III (Quantum Gravity)
Thomas Thiemann
Chair for Theoretical Physics III (Quantum Gravity)
Andreas Thurn
Chair for Theoretical Physics III (Quantum Gravity)

**APA:**

Bodendorfer, N., Thiemann, T., & Thurn, A. (2014). New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom. *Classical and Quantum Gravity*, *31*(5). https://dx.doi.org/10.1088/0264-9381/31/5/055002

**MLA:**

Bodendorfer, Norbert, Thomas Thiemann, and Andreas Thurn. "New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom." *Classical and Quantum Gravity* 31.5 (2014).

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